In accompany with the experiments, theoretical studies of DNA supercoiling have been developed based on the worm-like chain (WLC) model[1]}, [2]}, [3]}, [4]}, [5]}. The statistical mechanics of the WLC model of DNA provides a description of the coupling between supercoiling and DNA extension[3]}, [7]}, and reveals the pre-plectonemic loops formed by bending DNA, i.e., buckling transition[8]}, which give rise to the discontinuities on torque and extension versus linking number curves[9]}, [10]}. Further, studies show that under a stretching force, the coexistence of the S and P phases is maintained under a coexistence torque that is a function of the stretching force[4]}.
